THE SCIENCE OF GENDER AND SCIENCE

PINKER VS. SPELKE

A DEBATE

[5.16.2005]

...on the research on mind, brain, and behavior that may be relevant to gender disparities in the sciences, including the studies of bias, discrimination and innate and acquired difference between the sexes.

Harvard University • Mind/Brain/Behavior Initiative

The Mind Brain and Behavior Inter-Faculty Initiative (MBB), under the leadership of Co-Directors Marc D. Hauser and Elizabeth Spelke, is a university-wide community that studies the structure, function, evolution, development, and pathology of the nervous system, in relation to decision-making and behavior.

Introduction

On April 22, 2005, Harvard University's Mind/Brain/Behavior Initiative (MBB) held a defining debate on the public discussion that began on January 16th with the public comments by Lawrence Summers, president of Harvard, on sex differences between men and women and how they may relate to the careers of women in science. The debate at MBB, "The Gender of Gender and Science" was "on the research on mind, brain, and behavior that may be relevant to gender disparities in the sciences, including the studies of bias, discrimination and innate and acquired difference between the sexes".

It's interesting to note that since the controversy surrounding Summers' remarks began, there has been an astonishing absence of discussion of the relevant science...you won't find it in the hundreds and hundreds of articles in major newspapers; nor will find it in the Harvard faculty meetings where the president of the leading University in America was indicted for presenting controversial ideas.

Scientists debate continually, and reality is the check. They may have egos as large as those possessed by the iconic figures of the academic humanities, but they handle their hubris in a very different way. They can be moved by arguments, because they work in an empirical world of facts, a world based on reality. There are no fixed, unalterable positions. They are both the creators and the critics of their shared enterprise. Ideas come from them and they also criticize one another's ideas.

Through the process of creativity and criticism and debates, they decide which ideas get weeded out and which become part of the consensus that leads to the next level of discovery.

But unlike just about anything else said about Summers' remarks, the debate, "The Science of Gender and Science", between Harvard psychology professors Steven Pinker and Elizabeth Spelke, focused on the relevant scientific literature. It was both interesting on facts but differing in interpretation.

Both presented scientific evidence with the realization and understanding that there was nothing obvious about how the data was to be interpreted. Their sharp scientific debate informed rather than detracted. And it showed how a leading University can still fulfill its role of providing a forum for free and open discussion on controversial subjects in a fair-minded way. It also had the added benefit that the participants knew what they were talking about.

Who won the debate? Make up your own mind. Watch the video, listen to the audio, read the text and check out the slide presentations.

There's a lesson here: let's get it right and when we do we will adjust our attitudes. That's what science can do, and that's what Edge offers by presenting Pinker vs. Spelke to a wide public audience.

—JB

Steven Pinker's Edge Bio Page

ELIZABETH S. SPELKE is Berkman Professor of Psychology at Harvard University, where she is Co-Director of the Mind, Brain, and Behavior Initiative. A member of the National Academy of Sciences and the American Academy of Arts and Sciences, she is cited by Time Magazine as one of America's Best in Science and Medicine.

Elizabeth Spelke's Edge Bio Page

[EDITOR'S NOTE: Pinker and Spelke each made presentations of about 40 minutes, without interruption, from each other or from the audience. They then responded to each other's presentations. By mutual agreement, Pinker made the first presentation.

This Edge presentation includes: the transcribed text; streaming audio of the full debate; 6-minute video clips from Pinker and Spelke's opening statements; a 20-minute video clip of the their closing discussion; and online versions of the speakers' slide presentations. There are two options for viewing the slides: Clicking on the links immediately below brings up the file of either Pinker or Spelke's complete slide presentation. Or, the individual slides are also included for reference as expandable thumbnails in the margin of the transcript.]

PINKER slide presentation

SPELKE slide presentation

Steven Pinker [40 minutes] Streaming Audio Elizabeth Spelke [45 minutes] Streaming Audio Concluding Discussion [20 minutes] Streaming Audio	Steven Pinker: Opening Remarks [6 minute video] Broadband | Modem Elizabeth Spelke: Opening Remarks [6 minute video] Broadband | Modem     Steven Pinker & Elizabeth Spelke: Concluding Discussion [20 minute video] Broadband | Modem

The complete video, in .avi format, is also available for download through Harvard's MBB website (click here).

(STEVEN PINKER:) Thanks, Liz, for agreeing to this exchange. It's a privilege to be engaged in a conversation with Elizabeth Spelke. We go back a long way. We have been colleagues at MIT, where I helped attract her, and at Harvard, where she helped to attract me. With the rest of my field, I have enormous admiration for Elizabeth's brilliant contributions to our understanding of the origins of cognition. But we do find ourselves with different perspectives on a recent issue.

For those of you who just arrived from Mars, there has been a certain amount of discussion here at Harvard on a particular datum, namely the under-representation of women among tenure-track faculty in elite universities in physical science, math, and engineering. Here are some recent numbers:

As with many issues in psychology, there are three broad ways to explain this phenomenon. One can imagine an extreme "nature" position: that males but not females have the talents and temperaments necessary for science. Needless to say, only a madman could take that view. The extreme nature position has no serious proponents.

There is an extreme "nurture" position: that males and females are biologically indistinguishable, and all relevant sex differences are products of socialization and bias.

Then there are various intermediate positions: that the difference is explainable by some combination of biological differences in average temperaments and talents interacting with socialization and bias.

Liz has embraced the extreme nurture position. There is an irony here, because in most discussions in cognitive science she and I are put in the same camp, namely the "innatists," when it comes to explaining the mind. But in this case Liz has said that there is "not a shred of evidence" for the biological factor, that "the evidence against there being an advantage for males in intrinsic aptitude is so overwhelming that it is hard for me to see how one can make a case at this point on the other side," and that "it seems to me as conclusive as any finding I know of in science."

Well we certainly aren't seeing the stereotypical gender difference in confidence here! Now, I'm a controversial guy. I've taken many controversial positions over the years, and, as a member of Homo sapiens, I think I am right on all of them. But I don't think that in any of them I would say there is "not a shred of evidence" for the other side, even if I think that the evidence favors one side. I would not say that the other side "can't even make a case" for their position, even if I think that their case is not as good as the one I favor. And as for saying that a position is "as conclusive as any finding in science" — well, we're talking about social science here! This statement would imply that the extreme nurture position on gender differences is more conclusive than, say the evidence that the sun is at the center of the solar system, for the laws of thermodynamics, for the theory of evolution, for plate tectonics, and so on.

These are extreme statements — especially in light of the fact that an enormous amount of research, summarized in these and many other literature reviews, in fact points to a very different conclusion. I'll quote from one of them, a book called Sex Differences in Cognitive Ability by Diane Halpern. She is a respected psychologist, recently elected as president of the American Psychological Association, and someone with no theoretical axe to grind. She does not subscribe to any particular theory, and has been a critic, for example, of evolutionary psychology. And here what she wrote in the preface to her book:

"At the time I started writing this book it seemed clear to me that any between sex differences in thinking abilities were due to socialization practices, artifacts, and mistakes in the research. After reviewing a pile of journal articles that stood several feet high, and numerous books and book chapters that dwarfed the stack of journal articles, I changed my mind. The literature on sex differences in cognitive abilities is filled with inconsistent findings, contradictory theories, and emotional claims that are unsupported by the research. Yet despite all the noise in the data, clear and consistent messages could be heard. There are real and in some cases sizable sex differences with respect to some cognitive abilities. Socialization practices are undoubtedly important, but there is also good evidence that biological sex differences play a role in establishing and maintaining cognitive sex differences, a conclusion I wasn't prepared to make when I began reviewing the relevant literature."

This captures my assessment perfectly.

Again for the benefit of the Martians in this room: This isn't just any old issue in empirical psychology. There are obvious political colorings to it, and I want to begin with a confession of my own politics. I am a feminist. I believe that women have been oppressed, discriminated against, and harassed for thousands of years. I believe that the two waves of the feminist movement in the 20th century are among the proudest achievements of our species, and I am proud to have lived through one of them, including the effort to increase the representation of women in the sciences.

But it is crucial to distinguish the moral proposition that people should not be discriminated against on account of their sex — which I take to be the core of feminism — and the empirical claim that males and females are biologically indistinguishable. They are not the same thing. Indeed, distinguishing them is essential to protecting the core of feminism. Anyone who takes an honest interest in science has to be prepared for the facts on a given issue to come out either way. And that makes it essential that we not hold the ideals of feminism hostage to the latest findings from the lab or field. Otherwise, if the findings come out as showing a sex difference, one would either have to say, "I guess sex discrimination wasn't so bad after all," or else furiously suppress or distort the findings so as to preserve the ideal. The truth cannot be sexist. Whatever the facts turn out to be, they should not be taken to compromise the core of feminism.

Why study sex differences? Believe me, being the Bobby Riggs of cognitive science is not my idea of a good time. So should I care about them, especially since they are not the focus of my own research?

First, differences between the sexes are part of the human condition. We all have a mother and a father. Most of us are attracted to members of the opposite sex, and the rest of us notice the difference from those who do. And we can't help but notice the sex of our children, friends, and our colleagues, in every aspect of life.

Also, the topic of possible sex differences is of great scientific interest. Sex is a fundamental problem in biology, and sexual reproduction and sex differences go back a billion years. There's an interesting theory, which I won't have time to explain, which predicts that there should be an overall equal investment of organisms in their sons and daughters; neither sex is predicted to be superior or inferior across the board. There is also an elegant theory, namely Bob Trivers' theory of differential parental investment, which makes highly specific predictions about when you should expect sex differences and what they should look like.

The nature and source of sex differences are also of practical importance. Most of us agree that there are aspects of the world, including gender disparities, that we want to change. But if we want to change the world we must first understand it, and that includes understanding the sources of sex differences.

Let's get back to the datum to be explained. In many ways this is an exotic phenomenon. It involves biologically unprepared talents and temperaments: evolution certainly did not shape any part of the mind to do the work of a professor of mechanical engineering at MIT, for example. The datum has nothing to do with basic cognitive processes, or with those we use in our everyday lives, in school, or even in most college courses, where indeed there are few sex differences.

Also, we are talking about extremes of achievement. Most women are not qualified to be math professors at Harvard because most men aren't qualified to be math professors at Harvard. These are extremes in the population.

And we're talking about a subset of fields. Women are no under-represented to nearly the same extent in all academic fields, and certainly not in all prestigious professions.

Finally, we are talking about a statistical effect. This is such a crucial point that I have to discuss it in some detail.

Women are nowhere near absent even from the field in which they are most under-represented. The explanations for sex differences must be statistical as well. And here is a touchstone for the entire discussion:

These are two Gaussian or normal distributions; two bell curves. The X axis stands for any ability you want to measure. The Yaxis stands for the proportion of people having that ability. The overlapping curves are what you get whenever you compare the sexes on any measure in which they differ. In this example, if we say that this is the male curve and this is the female curve, the means may be different, but at any particular ability level there are always representatives of both genders.

So right away a number of public statements that have been made last couple of months can be seen as red herrings, and should never have been made by anyone who understands the nature of statistical distributions. This includes the accusation that President Summers implied that "50% of the brightest minds in America do not have the right aptitude for science," that "women just can't cut it," and so on. These statements are statistically illiterate, and have nothing to do with the phenomena we are discussing.

There are some important corollaries of having two overlapping normal distributions. One is that a normal distribution falls off according to the negative exponential of the square of the distance from the mean. That means that even when there is only a small difference in the means of two distributions, the more extreme a score, the greater the disparity there will be in the two kinds of individuals having such a score. That is, the ratios get more extreme as you go farther out along the tail. If we hold a magnifying glass to the tail of the distribution, we see that even though the distributions overlap in the bulk of the curves, when you get out to the extremes the difference between the two curves gets larger and larger.

For example, it's obvious that distributions of height for men and women overlap: it's not the case that all men are taller than all women. But while at five foot ten there are thirty men for every woman, at six feet there are two thousand men for every woman. Now, sex differences in cognition tend not to be so extreme, but the statistical phenomenon is the same.

With these statistical points in mind, let me begin the substance of my presentation by connecting the political issue with the scientific one. Economists who study patterns of discrimination have long argued (generally to no avail) that there is a crucial conceptual difference between difference and discrimination. A departure from a 50-50 sex ratio in any profession does not, by itself, imply that we are seeing discrimination, unless the interests and aptitudes of the two groups are equated. Let me illustrate the point with an example, involving myself.

I work in a scientific field — the study of language acquisition in children — that is in fact dominated by women. Seventy-five percent of the members the main professional association are female, as are a majority of the keynote speakers at our main conference. I'm here to tell you that it's not because men like me have been discriminated against. I decided to study language development, as opposed to, say, mechanical engineering, for many reasons. The goal of designing a better automobile transmission does not turn me on as much as the goal of figuring out how kids acquire language. And I don't think I'd be as good at designing a transmission as I am in studying child language.

Now, all we need to do to explain sex differences without invoking the discrimination or invidious sexist comparisons is to suppose that whatever traits I have that predispose me to choose (say) child language over (say) mechanical engineering are not exactly equally distributed statistically among men and women. For those of you out there — of either gender — who also are not mechanical engineers, you should understand what I'm talking about.

Indeed, in cases where there are differences, there are as many instances in which women do slightly better than men as ones in which men do slightly better than women. For example, men are better at throwing, but women are more dexterous. Men are better at mentally rotating shapes; women are better at visual memory. Men are better at mathematical problem-solving; women are better at mathematical calculation. And so on.

But there are at least six differences that are relevant to the datum we have been discussing. The literature on these differences is so enormous that I can only touch on a fraction of it. I'll restrict my discussion to a few examples in which there are enormous data sets, or there are meta-analyses that boil down a literature.

The first difference, long noted by economists studying employment practices, is that men and women differ in what they state are their priorities in life. To sum it up: men, on average, are more likely to chase status at the expense of their families; women give a more balanced weighting. Once again: Think statistics! The finding is not that women value family and don't value status. It is not that men value status and don't value family. Nor does the finding imply that every last woman has the asymmetry that women show on average or that every last man has the asymmetry that men show on average. But in large data sets, on average, an asymmetry what you find.

And this difference in interests will tend to cause people to gravitate in slightly different directions in their choice of career. The occupation that fits best with the "people" end of the continuum is "director of a community services organization." The occupations that fit best with the "things" end are physicist, chemist, mathematician, computer programmer, and biologist.

We see this consequence not only in the choice of whether to go into science, but also in the choice which branch of science the two sexes tend to go into. Needless to say, from 1970 to 2002 there was a huge increase in the percentage of university degrees awarded to women. But the percentage still differs dramatically across fields. Among the Ph.Ds awarded in 2001, for example, in education 65% of the doctorates went to women; in the social sciences, 54%; in the life sciences, 47%; in the physical sciences, 26%; in engineering, 17%. This is completely predictable from the difference in interests between people and living things, on the one hand, and inanimate objects, on the other. And the pattern is pretty much the same in 1980 and 2001, despite the change in absolute numbers.

I think the reason is that school grades are affected by homework and by the ability to solve the kinds of problems that have already been presented in lecture and textbooks. Whereas the aptitude tests are designed to test the application of mathematical knowledge to unfamiliar problems. And this, of course, is closer to the way that math is used in actually doing math and science.

Indeed, contrary to Liz, and the popular opinion of many intellectuals, the tests are surprisingly good. There is an enormous amount of data on the predictive power of the SAT. For example, people in science careers overwhelmingly scored in 90th percentile in the SAT or GRE math test. And the tests predict earnings, occupational choice, doctoral degrees, the prestige of one's degree, the probability of having a tenure-track position, and the number of patents. Moreover this predictive power is the same for men and for women. As for why there is that underprediction of grades — a slight under-prediction, one-tenth of a standard deviation — the Educational Testing Service did a study on that phenomenon, and were able to explain the mystery by a combination of the choice of major, which differs between the sexes, and the greater conscientiousness of women.

Second, many of the major sex differences — certainly some of them, maybe all of them, are universal. The idea that there are cultures out there somewhere in which everything is the reverse of here turns out to be an academic legend. In his survey of the anthropological literature called Human Universals, the anthropologist Donald Brown points out that in all cultures men and women are seen as having different natures; that there is a greater involvement of women in direct child care; more competitiveness in various measures for men than for women; and a greater spatial range traveled by men compared to by women.

In personality, we have a cross-national survey (if not a true cross-cultural one) in Feingold's meta-analysis, which noted that gender differences in personality are consistent across ages, years of data collection, educational levels, and nations. When it comes to spatial manipulation and mathematical reasoning, we have fewer relevant data, and we honestly don't have true cross-cultural surveys, but we do have cross-national surveys. David Geary and Catherine Desoto found the expected sex difference in mental rotation in ten European countries and in Ghana, Turkey, and China. Similarly, Diane Halpern, analyzing results from ten countries, said that "the majority of the findings show amazing cross-cultural consistency when comparing males and females on cognitive tests."

In tests of mental rotation, the meta-analysis by Voyer et al found no change over time. In mathematical reasoning there has been a decline in the size of the difference, although it has certainly not disappeared.

Fourth, many sex differences can be seen in other mammals. It would be an amazing coincidence if these differences just happened to be replicated in the arbitrary choices made by human cultures at the dawn of time. There are large differences between males and females in many mammals in aggression, in investment in offspring, in play aggression play versus play parenting, and in the range size, which predicts a species' sex differences in spatial ability (such as in solving mazes), at least in polygynous species, which is how the human species is classified. Many primate species even show a sex difference in their interest in physical objects versus conspecifics, a difference seen their patterns of juvenile play. Among baby vervet monkeys, the males even prefer to play with trucks and the females with other kinds of toys!

Fifth, many of these differences emerge in early childhood. It is said that there is a technical term for people who believe that little boys and little girls are born indistinguishable and are molded into their natures by parental socialization. The term is "childless."

Some sex differences seem to emerge even in the first week of life. Girls respond more to sounds of distress, and girls make more eye contact than boys. And in a study that I know Liz disputes and that I hope we'll talk about, newborn boys were shown to be more interested in looking at a physical object than a face, whereas newborn girls were shown to be more interested in looking at a face than a physical object.

A bit later in development there are vast and robust differences between boys and girls, seen all over the world. Boys far more often than girls engage in rough-and-tumble play, which involves aggression, physical activity, and competition. Girls spend a lot more often in cooperative play. Girls engage much more often in play parenting. And yes, boys the world over turn anything into a vehicle or a weapon, and girls turn anything into a doll. There are sex differences in intuitive psychology, that is, how well children can read one another's minds. For instance, several large studies show that girls are better than boys in solving the "false belief task," and in interpreting the mental states of characters in stories.

Sixth, genetic boys brought up as girls. In a famous 1970s incident called the John/Joan case, one member of a pair of identical twin boys lost his penis in a botched circumcision (I was relieved to learn that this was not done by a moyl, but by a bumbling surgeon). Following advice from the leading gender expert of the time, the parents agreed to have the boy castrated, given female-specific hormones, and brought up as a girl. All this was hidden from him throughout his childhood.

When I was an undergraduate the case was taught to me as proof of how gender roles are socially acquired. But it turned out that the facts had been suppressed. When "Joan" and her family were interviewed years later, it turned out that from the youngest ages he exhibited boy-typical patterns of aggression and rough-and-tumble play, rejected girl-typical activities, and showed a greater interest in things than in people. At age 14, suffering from depression, his father finally told him the truth. He underwent further surgery, married a woman, adopted two children, and got a job in a slaughterhouse.

This is not just a unique instance. In a condition called cloacal exstrophy, genetic boys are sometimes born without normal male genitalia. When they are castrated and brought up as girls, in 25 out of 25 documented instances they have felt that they were boys trapped in girls' bodies, and showed male-specific patterns of behavior such as rough-and-tumble play.

Seventh, a lack of differential treatment by parents and teachers. These conclusions come as a shock to many people. One comes from Lytton and Romney's meta-analysis of sex-specific socialization involving 172 studies and 28,000 children, in which they looked both at parents' reports and at direct observations of how parents treat their sons and daughters — and found few or no differences among contemporary Americans. In particular, there was no difference in the categories "Encouraging Achievement" and "Encouraging Achievement in Mathematics."

There is a widespread myth that teachers (who of course are disproportionately female) are dupes who perpetuate gender inequities by failing to call on girls in class, and who otherwise having low expectations of girls' performance. In fact Jussim and Eccles, in a study of 100 teachers and 1,800 students, concluded that teachers seemed to be basing their perceptions of students on those students' actual performances and motivation.

Eighth, studies of prenatal sex hormones: the mechanism that makes boys boys and girls girls in the first place. There is evidence, admittedly squishy in parts, that differences in prenatal hormones make a difference in later thought and behavior even within a given sex. In the condition called congenital adrenal hyperplasia, girls in utero are subjected to an increased dose of androgens, which is neutralized postnatally. But when they grow up they have male-typical toy preferences — trucks and guns — compared to other girls, male-typical play patterns, more competitiveness, less cooperativeness, and male-typical occupational preferences. However, research on their spatial abilities is inconclusive, and I cannot honestly say that there are replicable demonstrations that CAH women have male-typical patterns of spatial cognition.

A remark on stereotypes, and then I'll finish.

Are these stereotypes? Yes, many of them are (although, I must add, not all of them — for example, women's superiority in spatial memory and mathematical calculation. There seems to be a widespread assumption that if a sex difference conforms to a stereotype, the difference must have been caused by the stereotype, via differential expectations for boys and for girls. But of course the causal arrow could go in either direction: stereotypes might reflect differences rather than cause them. In fact there's an enormous literature in cognitive psychology which says that people can be good intuitive statisticians when forming categories and that their prototypes for conceptual categories track the statistics of the natural world pretty well. For example, there is a stereotype that basketball players are taller on average than jockeys. But that does not mean that basketball players grow tall, and jockeys shrink, because we expect them to have certain heights! Likewise, Alice Eagly and Jussim and Eccles have shown that most of people's gender stereotypes are in fact pretty accurate. Indeed the error people make is in the direction of underpredicting sex differences.

(ELIZABETH SPELKE:) Thanks, especially to Steve; I'm really glad we're able to have this debate, I've been looking forward to it.

I want to start by talking about the points of agreement between Steve and me, and as he suggested, there are many. If we got away from the topic of sex and science, we'd be hard pressed to find issues that we disagree on. Here are a few of the points of agreement that are particularly relevant to the discussions of the last few months.

First, we agree that both our society in general and our university in particular will be healthiest if all opinions can be put on the table and debated on their merits. We also agree that claims concerning sex differences are empirical, they should be evaluated by evidence, and we'll all be happier and live longer if we can undertake that evaluation as dispassionately and rationally as possible. We agree that the mind is not a blank slate; in fact one of the deepest things that Steve and I agree on is that there is such a thing as human nature, and it is a fascinating and exhilarating experience to study it. And finally, I think we agree that the role of scientists in society is rather modest. Scientists find things out. The much more difficult questions of how to use that information, live our lives, and structure our societies are not questions that science can answer. Those are questions that everybody must consider.

So where do we disagree?

We disagree on the answer to the question, why in the world are women scarce as hens' teeth on Harvard's mathematics faculty and other similar institutions? In the current debate, two classes of factors have been said to account for this difference. In one class are social forces, including overt and covert discrimination and social influences that lead men and women to develop different skills and different priorities. In the other class are genetic differences that predispose men and women to have different capacities and to want different things.

In his book, The Blank Slate, and again today, Steve argued that social forces are over-rated as causes of gender differences. Intrinsic differences in aptitude are a larger factor, and intrinsic differences in motives are the biggest factor of all. Most of the examples that Steve gave concerned what he takes to be biologically based differences in motives.

My own view is different. I think the big forces causing this gap are social factors. There are no differences in overall intrinsic aptitude for science and mathematics between women and men. Notice that I am not saying the genders are indistinguishable, that men and women are alike in every way, or even that men and women have identical cognitive profiles. I'm saying that when you add up all the things that men are good at, and all the things that women are good at, there is no overall advantage for men that would put them at the top of the fields of math and science.

On the issue of motives, I think we're not in a position to know whether the different things that men and women often say they want stem only from social forces, or in part from intrinsic sex differences. I don't think we can know that now.

I want to start with the issue that's clearly the biggest source of debate between Steve and me: the issue of differences in intrinsic aptitude. This is the only issue that my own work and professional knowledge bear on. Then I will turn to the social forces, as a lay person as it were, because I think they are exerting the biggest effects. Finally, I'll consider the question of intrinsic motives, which I hope we'll come back to in our discussion.

The first claim, as Steve said, is gaining new currency from the work of Simon Baron-Cohen. It's an old idea, presented with some new language. Baron-Cohen says that males are innately predisposed to learn about objects and mechanical relationships, and this sets them on a path to becoming what he calls "systematizers." Females, on the other hand, are innately predisposed to learn about people and their emotions, and this puts them on a path to becoming "empathizers." Since systematizing is at the heart of math and science, boys are more apt to develop the knowledge and skills that lead to math and science.

To anyone as old as I am who has been following the literature on sex differences, this may seem like a surprising claim. The classic reference on the nature and development of sex differences is a book by Eleanor Maccoby and Carol Jacklin that came out in the 1970s. They reviewed evidence for all sorts of sex differences, across large numbers of studies, but they also concluded that certain ideas about differences between the genders were myths. At the top of their list of myths was the idea that males are primarily interested in objects and females are primarily interested in people. They reviewed an enormous literature, in which babies were presented with objects and people to see if they were more interested in one than the other. They concluded that there were no sex differences in these interests.

Nevertheless, this conclusion was made in the early 70s. At that time, we didn't know much about babies' understanding of objects and people, or how their understanding grows. Since Baron-Cohen's claims concern differential predispositions to learn about different kinds of things, you could argue that the claims hadn't been tested in Maccoby and Jacklin's time. What does research now show?

Let me take you on a whirlwind tour of 30 years of research in one powerpoint slide. From birth, babies perceive objects. They know where one object ends and the next one begins. They can't see objects as well as we can, but as they grow their object perception becomes richer and more differentiated.

Babies also start with rudimentary abilities to represent that an object continues to exist when it's out of view, and they hold onto those representations longer, and over more complicated kinds of changes, as they grow. Babies make basic inferences about object motion: inferences like, the force with which an object is hit determines the speed with which it moves. These inferences undergo regular developmental changes over the infancy period.

In each of these cases, there is systematic developmental change, and there's variability. Because of this variability, we can compare the abilities of male infants to females. Do we see sex differences? The research gives a clear answer to this question: We don't.

Male and female infants are equally interested in objects. Male and female infants make the same inferences about object motion, at the same time in development. They learn the same things about object mechanics at the same time.

Across large numbers of studies, occasionally a study will favor one sex over the other. For example, girls learn that the force with which something is hit influences the distance it moves a month earlier than boys do. But these differences are small and scattered. For the most part, we see high convergence across the sexes. Common paths of learning continue through the preschool years, as kids start manipulating objects to see if they can get a rectangular block into a circular hole. If you look at the rates at which boys and girls figure these things out, you don't find any differences. We see equal developmental paths.

I think this research supports an important conclusion. In discussions of sex differences, we need to ask what's common across the two sexes. One thing that's common is infants don't divide up the labor of understanding the world, with males focusing on mechanics and females focusing on emotions. Male and female infants are both interested in objects and in people, and they learn about both. The conclusions that Maccoby and Jacklin drew in the early 1970s are well supported by research since that time.

As Steve said, formal mathematics is not something we have evolved to do; it's a recent accomplishment. Animals don't do formal math or science, and neither did humans back in the Pleistocene. If there is a biological basis for our mathematical reasoning abilities, it must depend on systems that evolved for other purposes, but that we've been able to harness for the new purpose of representing and manipulating numbers and geometry.

Research from the intersecting fields of cognitive neuroscience, neuropsychology, cognitive psychology, and cognitive development provide evidence for five "core systems" at the foundations of mathematical reasoning. The first is a system for representing small exact numbers of objects — the difference between one, two, and three. This system emerges in human infants at about five months of age, and it continues to be present in adults. The second is a system for discriminating large, approximate numerical magnitudes — the difference between a set of about ten things and a set of about 20 things. That system also emerges early in infancy, at four or five months, and continues to be present and functional in adults.

The third system is probably the first uniquely human foundation for numerical abilities: the system of natural number concepts that we construct as children when we learn verbal counting. That construction takes place between about the ages of two and a half and four years. The last two systems are first seen in children when they navigate. One system represents the geometry of the surrounding layout. The other system represents landmark objects.

All five systems have been studied quite extensively in large numbers of male and female infants. We can ask, are there sex differences in the development of any of these systems at the foundations of mathematical thinking? Again, the answer is no. I will show you data from just two cases.

These findings and others support two important points. First, indeed there is a biological foundation to mathematical and scientific reasoning. We are endowed with core knowledge systems that emerge prior to any formal instruction and that serve as a basis for mathematical thinking. Second, these systems develop equally in males and females. Ten years ago, the evolutionary psychologist and sex difference researcher, David Geary, reviewed the literature that was available at that time. He concluded that there were no sex differences in "primary abilities" underlying mathematics. What we've learned in the last ten years continues to support that conclusion.

Sex differences do emerge at older ages. Because they emerge later in childhood, it's hard to tease apart their biological and social sources. But before we attempt that task, let's ask what the differences are.

I think the following is a fair statement, both of the cognitive differences that Steve described and of others. When people are presented with a complex task that can be solved through multiple different strategies, males and females sometimes differ in the strategy that they prefer.

For example, if a task can only be solved by representing the geometry of the layout, we do not see a difference between men and women. But if the task can be accomplished either by representing geometry or by representing individual landmarks, girls tend to rely on the landmarks, and boys on the geometry. To take another example, when you compare the shapes of two objects of different orientations, there are two different strategies you can use. You can attempt a holistic rotation of one of the objects into registration with the other, or you can do point-by-point featural comparisons of the two objects. Men are more likely to do the first; women are more likely to do the second.

Finally, the mathematical word problems on the SAT-M very often allow multiple solutions. Both item analyses and studies of high school students engaged in the act of solving such problems suggest that when students have the choice of solving a problem by plugging in a formula or by doing Ven diagram-like spatial reasoning, girls tend to do the first and boys tend to do the second.

Because of these differences, males and females sometimes show differing cognitive profiles on timed tests. When you have to solve problems fast, some strategies will be faster than others. Thus, females perform better at some verbal, mathematical and spatial tasks, and males perform better at other verbal, mathematical, and spatial tasks. This pattern of differing profiles is not well captured by the generalization, often bandied about in the popular press, that women are "verbal" and men are "spatial." There doesn't seem to be any more evidence for that than there was for the idea that women are people-oriented and men are object-oriented. Rather the differences are more subtle.

Does one of these two profiles foster better learning of math than the other? In particular, is the male profile better suited to high-level mathematical reasoning?

At this point, we face a question that's been much discussed in the literature on mathematics education and mathematical testing. The question is, by what yardstick can we decide whether men or women are better at math?

Some people suggest that we look at performance on the SAT-M, the quantitative portion of the Scholastic Assessment Test. But this suggestion raises a problem of circularity. The SAT test is composed of many different types of items. Some of those items are solved better by females. Some are solved better by males. The people who make the test have to decide, how many items of each type to include? Depending on how they answer that question, they can create a test that makes women look like better mathematicians, or a test that makes men look like better mathematicians. What's the right solution?

Books are devoted to this question, with much debate, but there seems to be a consensus on one point: The only way to come up with a test that's fair is to develop an independent understanding of what mathematical aptitude is and how it's distributed between men and women. But in that case, we can't use performance on the SAT to give us that understanding. We've got to get that understanding in some other way. So how are we going to get it?

A second strategy is to look at job outcomes. Maybe the people who are better at mathematics are those who pursue more mathematically intensive careers. But this strategy raises two problems. First, which mathematically intensive jobs should we choose? If we choose engineering, we will conclude that men are better at math because more men become engineers. If we choose accounting, we will think that women are better at math because more women become accountants: 57% of current accountants are women. So which job are we going to pick, to decide who has more mathematical talent?

These two examples suggest a deeper problem with job outcomes as a measure of mathematical talent. Surely you've got to be good at math to land a mathematically intensive job, but talent in mathematics is only one of the factors influencing career choice. It can't be our gold standard for mathematical ability.

So what can be? I suggest the following experiment. We should take a large number of male students and a large number of female students who have equal educational backgrounds, and present them with the kinds of tasks that real mathematicians face. We should give them new mathematical material that they have not yet mastered, and allow them to learn it over an extended period of time: the kind of time scale that real mathematicians work on. We should ask, how well do the students master this material? The good news is, this experiment is done all the time. It's called high school and college.

Here's the outcome. In high school, girls and boys now take equally many math classes, including the most advanced ones, and girls get better grades. In college, women earn almost half of the bachelor's degrees in mathematics, and men and women get equal grades. Here I respectfully disagree with one thing that Steve said: men and women get equal grades, even when you only compare people within a single institution and a single math class. Equating for classes, men and women get equal grades.

The outcome of this large-scale experiment gives us every reason to conclude that men and women have equal talent for mathematics. Here, I too would like to quote Diane Halpern. Halpern reviews much evidence for sex differences, but she concludes, "differences are not deficiencies." Men and women have equal aptitude for mathematics. Yes, there are sex differences, but they don't add up to an overall advantage for one sex over the other.

Let me turn to the third claim, that men show greater variability, either in general or in quantitative abilities in particular, and so there are more men at the upper end of the ability distribution. I can go quickly here, because Steve has already talked about the work of Camilla Benbow and Julian Stanley, focusing on mathematically precocious youth who are screened at the age of 13, put in intensive accelerated programs, and then followed up to see what they achieve in mathematics and other fields.

As Steve said, students were screened at age 13 by the SAT, and there were many more boys than girls who scored at the highest levels on the SAT-M. In the 1980s, the disparity was almost 13 to 1. It is now substantially lower, but there still are more boys among the very small subset of people from this large, talented sample who scored at the very upper end. Based on these data, Benbow and Stanley concluded that there are more boys than girls in the pool from which future mathematicians will be drawn. But notice the problem with this conclusion: It's based entirely on the SAT-M. This test, and the disparity it revealed, are in need of an explanation, a firmer yardstick for assessing and understanding gender differences in this talented population.

Fortunately, Benbow, Stanley and Lubinski have collected much more data on these mathematically talented boys and girls: not just the ones with top scores on one timed test, but rather the larger sample of girls and boys who were accelerated and followed over time. Let's look at some of the key things that they found.

First, they looked at college performance by the talented sample. They found that the males and females took equally demanding math classes and majored in math in equal numbers. More girls majored in biology and more boys in physics and engineering, but equal numbers of girls and boys majored in math. And they got equal grades. The SAT-M not only under-predicts the performance of college women in general, it also under-predicted the college performance of women in the talented sample. These women and men have been shown to be equally talented by the most meaningful measure we have: their ability to assimilate new, challenging material in demanding mathematics classes at top-flight institutions. By that measure, the study does not find any difference between highly talented girls and boys.

So, what's causing the gender imbalance on faculties of math and science? Not differences in intrinsic aptitude. Let's turn to the social factors that I think are much more important. Because I'm venturing outside my own area of work, and because time is short, I won't review all of the social factors producing differential success of men and women. I will talk about just one effect: how gender stereotypes influence the ways in which males and females are perceived.

Let me start with studies of parents' perceptions of their own children. Steve said that parents report that they treat their children equally. They treat their boys and girls alike, and they encourage them to equal extents, for they want both their sons and their daughters to succeed. This is no doubt true. But how are parents perceiving their kids?

Some studies have interviewed parents just after the birth of their child, at the point where the first question that 80% of parents ask — is it a boy or a girl? — has been answered. Parents of boys describe their babies as stronger, heartier, and bigger than parents of girls. The investigators also looked at the babies' medical records and asked whether there really were differences between the boys and girls in weight, strength, or coordination. The boys and girls were indistinguishable in these respects, but the parents' descriptions were different.

At 12 months of age, girls and boys show equal abilities to walk, crawl, or clamber. But before one study, Karen Adolph, an investigator of infants' locomotor development, asked parents to predict how well their child would do on a set of crawling tasks: Would the child be able to crawl down a sloping ramp? Parents of sons were more confident that their child would make it down the ramp than parents of daughters. When Adolph tested the infants on the ramp, there was no difference whatever between the sons and daughters, but there was a difference in the parents' predictions.

My third example, moving up in age, comes from the studies of Jackie Eccles. She asked parents of boys and girls in sixth grade, how talented do you think your child is in mathematics? Parents of sons were more likely t